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Calculated Microwave Absorption by DoubleHelical DNA M. KOHLI, W. N. MEI, L. L. VAN ZANDT, and E. W. PROHOFSKY Downloaded by STONY BROOK UNIV SUNY on October 6, 2017 | http://pubs.acs.org Publication Date: August 4, 1981 | doi: 10.1021/bk-1981-0157.ch007

Department of Physics, Purdue University, West Lafayette, IN 47907

The direct absorption of moderate to low frequency, non ionizing, electromagnetic radiation - microwaves - by DNA polymer molecules is a potential source of biological effects. As an introductory study of this question, we have evaluated the ab sorption of isolated homopolymer straight chains of poly dG-poly dC. For some absorption processes we have also investigated some effects of a surrounding aqueous medium. The effect of absorbing a microwave photon by a molecule is to excite one of the fundamental normal modes of the molecular vibration. On a long polymer chain these normal modes correspond to traveling waves of varying wavelengths and corresponding fre quencies as well as different relative motions of the atoms with in a monomeric unit. It is convenient to group together the modes of similar monomeric atomic displacements into bands of modes. Within a band, the modes are individually specified by a wavelength parameter, θ. θ varies in small but discrete steps from 0 to ±π; each different value of θ corresponds to a differ ent number of half wavelengths on the total chain length. On a very long chain, θ values corresponding to very few half wavelengths (i.e., long wavelengths) label motion in which the atoms of neighboring monomers execute very nearly the same motions simultaneously. At infinite wavelength, the motions of neighboring monomers are exactly identical. The simplest case of this kind of motion occurs when the chain as a whole is uniform ly translated, or rotated about the central axis. Since no rela tive atomic positions are changed in this type of displacement, no restoring forces between atoms arise from i t . Viewed as a type of normal mode motion, these displacements have zero force constants and therefore zero frequency. Also, the bands of nor mal modes in which they are grouped will a l l be of relatively low frequency. The structure of the lowest frequency vibrational bands of a helical chain is shown in Figure 1. The two zero frequency modes at θ = 0 correspond to rotation and translation along the central helical axis. Translations perpendicular to the helical axis are 0097-6156/81/0157-0101$05.00/0 © 1981 American Chemical Society

Illinger; Biological Effects of Nonionizing Radiation ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

Downloaded by STONY BROOK UNIV SUNY on October 6, 2017 | http://pubs.acs.org Publication Date: August 4, 1981 | doi: 10.1021/bk-1981-0157.ch007

102

BIOLOGICAL EFFECTS OF NONIONIZING

RADIATION

described by the modes a t θ = + 36°, the h e l i x p i t c h angle; that these occur a t + 36° i n s t e a d of 0 i s a consequence of the t w i s t i n the s t r u c t u r e . The curves i n f i g u r e 1 are i n f a c t our computed s t r u c t u r e of normal mode frequencies of poly(dG)-poly(dC) double h e l i x ( 1 ) . Modes near θ = 0 have c h a r a c t e r i s t i c motions corresponding to g e n t l e t w i s t i n g of the chain ( i . e . , o v e r a l l r o t a t i o n of the chain by d i f f e r e n t amounts i n separated r e g i o n s ) and g e n t l e compression ( o v e r a l l t r a n s l a t i o n by d i f f e r e n t amounts i n separated regions.) The modes near θ = + 36° correspond t o t r a n s v e r s e displacements by d i f f e r i n g amounts i n separated r e g i o n s . This motion i s best d e s c r i b a b l e as a bending of the c h a i n . For modes f u r t h e r removed from θ = + 36°, a c e r t a i n amount of shearing motion accompanies the bending. In a long wavelength t o r s i o n a l or compressional motion, the displacement of the molecule r e q u i r e s r e l a t i v e l y l i t t l e motion of the surrounding s o l v e n t ; i n the course of the motion, each por t i o n of the molecule i s c a r r i e d i n t o a volume p r e v i o u s l y occupied by another p o r t i o n of the molecule. I n c o n t r a s t to t h i s , the t r a n s v e r s e displacement "bending" modes r e q u i r e that surrounding water be d i s p l a c e d ; the molecule moves i n t o and out o f , spaces formerly occupied by s o l v e n t . We have used the known e l a s t i c p r o p e r t i e s of b u l k water at long wavelengths to c a l c u l a t e the c o r r e c t i o n t o the normal mode frequencies of the t r a n s v e r s e displacements. Damping and asso c i a t e d frequency p u l l i n g by water v i s c o s i t y has been l e f t out of a l l modes. The a l t e r e d frequencies of the t r a n s v e r s e modes are d i s p l a y e d i n f i g u r e 1 and c o n t r a s t e d w i t h the frequencies of the bending molecule i n vacuo. S i m i l a r c a l c u l a t i o n s on the l o n g i t u d i n a l mode show that the frequency of that mode i s not changed by the c o u p l i n g of the molecule w i t h the medium. Methods The double h e l i x has unbalanced charge on many atoms. The displacements a s s o c i a t e d w i t h v i b r a t i o n a l modes generate o s c i l l a t i n g d i p o l e moments. These moments are constructed from our eigenvector displacements and models of atomic net charge taken from the l i t e r a t u r e (2, 3 ) . These d i p o l e moment m a t r i x elements have been c a l c u l a t e d ( 4 ) . The E i n s t e i n c o e f f i c i e n t of a b s o r p t i o n of r a d i a t i o n f o r the l o n g i t u d i n a l (along the ζ a x i s ) and the t r a n s v e r s e (perpendicu l a r to the ζ a x i s ) electromagnetic f i e l d s can be obtained from these m a t r i x elements and are given by (1)

(2) where I r e f e r s to a p a r t i c u l a r band.


7.

KOHLI ET AL.

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Microwave Absorption by Double-Helical DNA


These c o e f f i c i e n t s can be evaluated f o r any biopolymer by taking an a r b i t r a r y chain length and determining the allowed values of frequencies f o r any s e t of boundary c o n d i t i o n s . I n our c a l c u l a t i o n s we have assumed that the ends of the chain are f i x e d and we determine the frequency of the modes that permit an odd number of h a l f wavelengths to be present on the c h a i n . The eigen v e c t o r s f o r these frequencies a r e determined from the d i s p e r s i o n curves f o r an i n f i n i t e c h a i n . To make these c a l c u l a t i o n s more compatible w i t h experiment we have determined the a b s o r p t i o n cross s e c t i o n which can be r e l a t e d t o the E i n s t e i n c o e f f i c i e n t by the f o l l o w i n g expression a(v) = - = - Β S(v) . IN C ο

(3)

Here k i s the a b s o r p t i o n c o e f f i c i e n t a t frequency v, N i s the number of absorbing centres per cubic centimeter, ν i s the f r e quency o f a b s o r p t i o n , and S(v) i s the l i n e shape f u n c t i o n . F o r our estimates we s h a l l assume that the l i n e shape i s L o r e n t z i a n having h a l f width 6 . I f one evaluates the a b s o r p t i o n cross s e c t i o n when the a b s o r p t i o n i s maximum the above expression takes the form 1 u , ν I n max •, \ a (ν) = — Β . (4) max π c 6v

Q

L

v

The s i g n i f i c a n c e of the above t h e o r e t i c a l estimates of the a b s o r p t i o n cross s e c t i o n l i e s i n comparing the a b s o r p t i o n of the incoming r a d i a t i o n by the biopolymer w i t h that of the surrounding medium (water). The a b s o r p t i o n cross s e c t i o n f o r water i n the microwave frequency range can be obtained from the d i e l e c t r i c d i s p e r s i o n data (5) by using the f o l l o w i n g expression a(v) = N.,

= -i N-,

,

(5)

nc

1 1

where ε i s the imaginary part of the d i e l e c t r i c constant a t the frequency ν, η i s the r e f r a c t i v e index at the same frequency, and the number of molecules of water per cubic centimetre. In our model the a b s o r p t i o n i s a maximum when a s o n i c h a l f wavelength i s equal to the length of the f i n i t e h e l i x . The ab s o r p t i o n approaches zero f o r h e l i x length equal t o a whole wave l e n g t h . The a b s o r p t i o n i s l a r g e again f o r (3/2)λ = L e t c . We p l o t the envelope of these absorption peaks (per base p a i r ) f o r the a c o u s t i c modes as a f u n c t i o n of frequency from Eq. (4) i n F i g . 2 f o r h e l i x segments of 51 and 451 base p a i r s i n l e n g t h . The f i g u r e shows the a b s o r p t i o n f o r a l l the a c o u s t i c modes. We have assumed a l i n e width of 10% f o r use i n Eq. (4). Larger l i n e widths cannot e f f e c t the r e s u l t by more than order of magnitude.


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BIOLOGICAL

E F F E C T S O F NONIONIZING RADIATION


1800.

100

200

30.0

40.0

500

Angle (Degrees)

Figure 1. Calculated frequency vs. phase shift θ dispersion curves for the two lowest bands in poly(dG)-poly(dC) in Β conformation based on recent refinements. The more steeply rising curve is the longitudinal or compression mode. The less steep curve at θ ̶ 0 is the torsional mode. The quadratic curves at θ = 36 are beam bending modes. The dashed curve is the dispersion obtained after taking into account the cou pling to water.

\ • \

\ Bending \Mode V M N B = 5I)

Longitudinal \ ^ Acoustic \ \ ( N B = 5I)

"XBending \Mode ^è

Calculated Microwave Absorption by Double ... - ACS Publications

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